Fully coupled finite element model for dynamics of partially saturated soils

Understanding the response of partially saturated earth structures under various static and dynamic loads is important for the design and construction of economical and safe geotechnical engineering structures. In this study, the numerical approach is used to understand the dynamics of partially saturated soils. The mathematical equations governing the dynamics of partially saturated soils are derived based on the theory of mixtures and implemented within a finite element framework. The stress–strain behavior of the soil is represented by an elasto-plastic constitutive model for unsaturated soil based on bounding surface concept and the moisture-suction behavior is modeled using van Genuchten model. Fully coupled finite element simulations are performed to study the response of partially saturated soil embankment under earthquake loading and validated with centrifuge test results available in the literature. The predicted displacement responses are in good agreement with the measured responses. The pore water pressure, pore air pressure, matric suction, the degree of saturation in various elements and the response of the embankment under different initial moisture content are also discussed.     

The Interface Configuration of the Fresh‐/Dead Sea Water – Theory and Measurements

The high‐density Dead Sea water (1.235 g/cm³) forms a special interface configuration with the fresh groundwater resources of its surrounding aquifers. The fresh groundwater column beneath its surroundings is around one tenth of its length compared to oceanic water. This fact alone indicates the vulnerability of the fresh groundwater resources to the impacts of changes in the Dead Sea level and to saltwater migration. Ghyben‐Herzberg and Glover equations were used to calculate the volumes of water in coastal aquifers which were replaced by freshwater due to the interface seaward migration as a result of the drop in the level of the Dead Sea. For that purpose, the dynamic equation of Glover approach has been integrated to accommodate that type of interface readjustment. The calculated amounts of freshwater which substituted salt Dead Sea water due to the migration of interface are 3.21 · 10¹¹ m³, from a Dead Sea level of –392 m to τ411 m below sea level. The average porosity of coastal aquifers was calculated to range from 2.8 to 2.94%. Geoelectric sounding measurements showed that areas underlying the coastal aquifers formerly occupied by the Dead Sea water are gradually becoming flushed and occupied by freshwater. The latter is becoming salinized due to the residuals of Dead Sea water in the aquifer matrix, the present salinity of which is lower than that of the Dead Sea water. At the same time salt dissolution from the Lisan Marl formation is causing collapses along the shorelines in the form of sinkholes, tens of meters in diameter and depth.     

Effect of impervious members and reservoir bottom sediment on dynamic response of embankment dams

In this paper, a systematic investigation into the effect of both the type of impervious members and the reservoir bottom sediment on the dynamic response of embankment dams has been carried out using the finite and infinite element coupled method. It has been demonstrated from the numerical results that: (1) the resonant frequencies of an embankment dam—foundation system with an upstream inclined concrete apron are different from those with a central clay core; (2) the type of impervious members has a significant influence on the amplification factors of the system in the low frequency range of excitation, but has little effect in the high frequency range of excitation; (3) the foundation material of an embankment dam affects the dynamic response of the dam drastically; (4) the inclusion of the reservoir bottom sediment has a considerable effect on amplification factors of embankment dams in the case of P-wave incidences, but has little influence in the case of SV-wave vertical incidences; and (5) the reservoir bottom sediment also has a profound effect on the deformed shape of the embankment dam for both P-wave and SV-wave incidences.     

H-adaptivity applied to liquefiable soil in nonlinear analysis of soil–pile interaction

This paper is concerned with application of the h-adaptive finite element method to dynamic analysis of a pile in liquefiable soil considering large deformation. In finite element analysis of pile behavior in liquefiable soil during an earthquake, especially considering large deformation of liquefied ground, error due to discretization in the zone near the pile becomes very large. Our purpose was to refine the approximation of the finite element method. The updated Lagrangian formulation and a cyclic elasto-plastic model based on the kinematic hardening rule were adopted to deal with the nonlinearity of the soil. The mixed finite element and finite difference methods together with the u-p formulation and Biot's two-phase mixture theory were used. To improve the accuracy and increase the efficiency of finite element analysis, an h-adaptive scheme that included a posteriori error estimation and h-version mesh refinement was applied to the analysis. The calculated results of effective stress were smoothed locally by the extrapolation method and smoothed stress was used to calculate the L₂ norm of the effective stress error in the last step of the calculation of each time increment. The mesh was refined by a fission procedure based on the indication of the error estimate As a numerical example, a soil–pile interaction system loaded cyclically was analyzed by our method.     

Bridge–embankment interaction under transverse ground excitation

Seismic performance and dynamic response of bridge–embankments during strong or moderate ground excitations are investigated through finite element (FE) modelling and detailed dynamic analysis. Previous research studies have established that bridge–embankments exhibit increasingly flexible performance under high‐shear deformation levels and that soil displacements at bridge abutment supports may be significant particularly in the transverse direction. The 2D equation of motion is solved for the embankment, in order to evaluate the dynamic characteristics and to describe explicitly the seismic performance and dynamic response under transverse excitations accounting for soil nonlinearities, soil–structure interaction and imposed boundary conditions (BCs). Using the proposed model, equivalent elastic analysis was performed so as to evaluate the dynamic response of approach embankments while accounting for soil–structure interaction. The analytical procedures were applied in the case of a well‐documented bridge with monolithic supports (Painter Street Overcrossing, PSO) which had been instrumented and embankment participation was identified from its response records after the 1971 San Fernando earthquake. The dynamic characteristics and dynamic response of the PSO embankments were evaluated for alternative BCs accounting for soil–structure interaction. Explicit expressions for the evaluation of the critical embankment length L_c are provided in order to quantify soil contribution to the overall bridge system under strong intensity ground excitations. The dynamic response of the entire bridge system (deck–abutments–embankments) was also evaluated through simplified models that considered soil–structure interaction. Results obtained from this analysis are correlated with those of detailed 3D FE models and field data with good agreement. Copyright © 2007 John Wiley & Sons, Ltd.     

Seismic response of offshore structures in random seas

A study of the dynamic response of offshore structures to simultaneous loadings by random earthquake ground motions and random sea waves is presented. Emphasis is placed on the evaluation of dynamic soil-structure interaction effects and also on the evaluation of non-linear hydrodynamic damping effects due to sea waves for the seismic response. The structure is discretized using the finite element method. Sea waves are represented by Bretschneider's power spectrum and the Morison equation defines the wave forcing function. The Tajimi-Kanai power spectrum is used for the horizontal ground acceleration due to earthquakes. The governing equations of motion are obtained by the substructure method. Response analysis is carried out using the frequency-domain random vibration approach. It is found that the first few vibrational modes contribute significantly to the dynamic response. The response due to earthquake loadings is larger when the soil-structure interaction effects are considered. The hydrodynamic damping forces are higher in random seas than in still water and sea waves reduce the seismic response of offshore structures. Studies on the first passage probabilities of response indicate that small sea waves enhance the reliability of offshore structures against earthquake forces.     

列车荷载下巴准重载铁路高路堤路基累积变形研究

针对巴准重载铁路高路堤典型断面,采用三维非线性有限元与经验公式相结合的方法,建立了可考虑列车-轨道动力相互作用的重载列车振动荷载引起的高路堤路基累积变形计算方法。首先,基于列车-轨道垂向耦合动力系统理论,建立重载列车-轨道动力耦合体系数值模型,并实施重载列车-轨道耦合系统动力分析;其次,建立轨枕-道床-路基-场地动力系统的三维有限元模型,并输入求解的列车振动荷载作为外部激励;最后,采用Li和Selig推荐的改进土体累积变形预测模型并结合有限元分析结果,分析了未加固和应用土工格栅加固的高路堤路基累积变形的基本特征与规律。发现土工格栅可显著减小路基的动力累积变形作用。     

Fully coupled numerical analysis of repeated shake-consolidation process of earth embankment on liquefiable foundation

It is known that a series of aftershocks might follow a mainshock, which may cause further damages on civil engineering structures. So it is necessary to investigate the dynamic response of structures undergone several shocks. This study presents a numerical analysis of repeated shake-consolidation process for an earth embankment founded on liquefiable foundation soils. Analysis is carried out using an effective stress-based, fully coupled, finite element method. The behaviors of the foundation soils are described by means of a cyclic mobility constitutive model which was developed at the bases of modified Cam-clay model by introducing concepts such as stress-induced anisotropy, over-consolidation, and structure. Results show that the cyclic mobility constitutive model can reflect the dynamic response of liquefiable soils. Special emphasis is given to analyze the result of excess pore water pressures, stress path, acceleration, and deformations during the two seismic excitation and consolidation process.     

Axisymmetric soil–structure interaction by global–local finite elements

A version of the global–local finite element method is presented for studying dynamic steady-state soil–structure interaction wherein the soil medium extends to infinity. Herein, only axisymmetric behaviour is considered. In this approach, conventional finite elements are used to model the structure and some portion of the surrounding soil medium considered to be homogeneous and isotropic. A complete set of outgoing waves in the form of spherical harmonics for the entire space is used to represent the behaviour in the half-space beyond the finite element mesh and these are termed the global functions. Full traction and displacement continuity is enforced at the finite element mesh interface with the outer region. On the free surface of the half-space in the outer field, traction-free surface conditions are enforced by demanding that a sequence of integrals of the weighted-average tractions must vanish. Numerical examples are presented for the response of different shaped foundations, resting on the free surface or at various submerged levels, due to a normal seismic plane compressional wave. Plots of differential scattering cross-sections show the angular distribution of the energy (its directional nature) of the scattered field.     

Asymptotic formulae for correcting finite element predicted natural frequencies of gravity and embankment dams

Extraction of natural frequencies of a gravity dam or an embankment dam plays an important role in the seismic design of the dam because the seismic response of a dam is dependent largely on the dynamic characteristics of the dam. Owing to the lack of exact solutions and the geometry of a dam, numerical methods such as finite element methods have been often used to extract the natural frequencies of the dam. Since the finite element method is an approximate one, the resulting finite element solution to the natural frequency of a dam cannot be safely used unless its accuracy is evaluated within the acceptable range for the seismic design of the dam. To solve this problem, some asymptotic formulae for correcting the finite element predicted natural frequencies of a gravity dam and an embankment dam have been developed in this paper. Since the present asymptotic formulae are derived from the fact that the finite element solution tends to the exact one if the finite element size used approaches zero, they provide a corrected solution of higher accuracy for the natural frequency of a dam so that the accuracy of a finite element solution can be evaluated against this corrected solution. After the correctness and usefulness of the present formulae are assessed, two practical examples have been given to show how the asymptotic formulae can be used to correct and evaluate the discretization error for the finite element predicted natural frequencies of gravity dams and embankment dams.     

An explicit finite element method for dy—namic analysis in three—medium coupling system and its application

In this paper,an explicit finite element method to analyze the dynamic responses of three-medium coupled systems with any terrain is developed on the basis of the numerical simulation of the continuous conditions on the bounda-ries among fluid saturated porous medium,elastic single-phase medium and ideal fluid medium.This method is a very effective one with the characteristic of high calculating speed and small memory needed because the formulae for this explicit finite element method have the characteristic of decoupling,and which does not need to solve sys-tem of linear equations.The method is applied to analyze the dynamic response of a reservoir with considering the dynamic interactions among water,dam,sediment and basement rock.The vertical displacement at the top point of the dam is calculated and some conclusions are given.     

三种介质耦联系统动力反应分析的显式有限元法及其应用

在笔者已建立的流体饱和多孔介质动力分析的显式有限元法的基础上，提出了可分析任意形状的流体饱和多孔介质-单相弹性固体介质-理想流体介质耦联的复杂系统的动力响应的显式有限元方法．该方法建立的有限元方程列式具有解耦特征，不需求解联立方程组，因而极大地提高了计算效率．将这一方法用于分析了考虑库水、坝、淤泥层和基岩这一复杂系统动力相互作用问题的斜坝面的地震响应，并给出了一些计算结果．      

Causes for the decline of suspended‐sediment discharge in the Mississippi River system, 1940–2007

Before 1900, the Missouri–Mississippi River system transported an estimated 400 million metric tons per year of sediment from the interior of the United States to coastal Louisiana. During the last two decades (1987–2006), this transport has averaged 145 million metric tons per year. The cause for this substantial decrease in sediment has been attributed to the trapping characteristics of dams constructed on the muddy part of the Missouri River during the 1950s. However, reexamination of more than 60 years of water‐ and sediment‐discharge data indicates that the dams alone are not the sole cause. These dams trap about 100–150 million metric tons per year, which represent about half the decrease in sediment discharge near the mouth of the Mississippi. Changes in relations between water discharge and suspended‐sediment concentration suggest that the Missouri–Mississippi has been transformed from a transport‐limited to a supply‐limited system. Thus, other engineering activities such as meander cutoffs, river‐training structures, and bank revetments as well as soil erosion controls have trapped sediment, eliminated sediment sources, or protected sediment that was once available for transport episodically throughout the year. Removing major engineering structures such as dams probably would not restore sediment discharges to pre‐1900 state, mainly because of the numerous smaller engineering structures and other soil‐retention works throughout the Missouri–Mississippi system. Published in 2009 by John Wiley & Sons, Ltd.     

Reconstruction of eroded and deposited sediment volumes of the embanked River Waal,the Netherlands,for the period ad 1631–present

In the last few centuries humans have modified rivers, and rivers have responded with noticeable changes in sedimentary dynamics. The objective of this study is to assess these responses of the sedimentary dynamics. Therefore, we calculated a sediment budget for eroded and deposited sediment volumes in a ~12‐km long floodplain section of the largest semi‐natural embanked but still dynamic lower Rhine distributary, for ~50‐years time slices between ad 1631 and present. This is the period during which embanked floodplains were formed by downstream migration of meander bends between confining dykes. Our sediment budget involves a detailed reconstruction of vertical and lateral accretion rates and erosion rates of floodplain sediment. To do so, we developed a series of historical geomorphological maps, and lithogenetic cross‐sections. Based on the maps and cross‐sections, we divided the floodplain into building blocks representing channel bed and overbank sediment bodies. Chronostratigraphy within the blocks was estimated by interpretation of heavy metal profiles and from optically stimulated luminescence (OSL) dating results. Sediment budgets were hence calculated as a change of volume of each building block between time steps. The amount of lateral accretion initially increased, as a result of island and sand bar formation following embankment. From the eighteenth century onwards, there was a decrease of lateral processes in time, which is a result of straightening of the river by human activities, and a reduction of water and sediment supply due to the construction of a new upstream bifurcation. With straightening of the river, the floodplain area grew. Artificial fixation of the channel banks after ad 1872 prevented lateral activity. From then on, overbank deposition became the main process, leading to a continuous increase of floodplain elevation, and inherent decrease of flooding frequency and sediment accumulation rate. Copyright © 2014 John Wiley & Sons, Ltd.     

Dynamic soil–structure interaction analysis via coupled finite-element–boundary-element method

In this paper, a study on the transient response of an elastic structure embedded in a homogeneous, isotropic and linearly elastic half-plane is presented. Transient dynamic and seismic forces are considered in the analysis. The numerical method employed is the coupled Finite-Element–Boundary-Element technique (FE–BE). The finite element method (FEM) is used for discretization of the near field and the boundary element method (BEM) is employed to model the semi-infinite far field. These two methods are coupled through equilibrium and compatibility conditions at the soil–structure interface. Effects of non-zero initial conditions due to the pre-dynamic loads and/or self-weight of the structure are included in the transient boundary element formulation. Hence, it is possible to analyse practical cases (such as dam–foundation systems) involving initial conditions due to the pre-seismic loads such as water pressure and self-weight of the dam. As an application of the proposed formulation, a gravity dam has been analysed and the results for different foundation stiffness are presented. The results of the analysis indicate the importance of including the foundation stiffness and thus the dam–foundation interaction.     

地震荷载作用下带裂纹重载铁路隧道的动态断裂

在隧道的施工和运营中,隧道衬砌不可避免会产生裂纹。裂纹和地震荷载的相互作用将加剧隧道的破坏,因此研究带裂纹隧道衬砌地震荷载作用下的破坏具有重要的意义。为了证明本文二维有限元数值模拟计算结果的正确性,首先用相互作用积分的方法计算动载作用下的静态裂纹,并与解析解进行比对,发现二者的吻合性很好。计算结果表明相互作用积分法可以用来精确地计算动载作用下带裂纹结构的动应力强度因子。用这种经过验证的方法来计算带裂纹重载铁路隧道衬砌的动应力强度因子和动承载力安全系数,可以看出在地震荷载作用下,I型裂纹的动应力强度因子在隧道结构的安全中起控制作用。当裂纹的长度大于某特定值时,隧道处于很危险的状态。     

The impact of reed-protecting structures on littoral zones

The impact of several types of reed-protecting structures on hydrodynamic conditions, sediment properties and littoral water quality were investigated. All types of embankment lead to a dissipation of wave energy. The embankment with fagots (type 1) shows a limited porosity in contrast to the other types examined. All kinds of embankment enhance the accumulation of organic matter at the land/water-interface. Hence, they protect littoral accumulation zones from erosion. The embankment with fagots causes changes in sediment properties at the seaward side of reed belts. The surface of mineral sediments is turned into a fine-grained mud, with a high content of organic matter. Accelerated sedimentary microbial processes (oxygen demand) are produced by increasing nutrient availability (carbon, nitrogen). As a result, the O₂-saturation of water bodies is significantly reduced. This is in contrast to the embankment with wooden partitions and palisades (type 2 and 3), which had no significant effects on sediment conditions and water quality. The consequences of changes in type 1-protected reed stands are discussed. Practical recommendations are given for the further use of reed-protecting structures.     

Influence of Seasonal Variations in Sea Level on the Salinity Regime of a Coastal Groundwater–Fed Wetland

Seasonal variations in sea level are often neglected in studies of coastal aquifers; however, they may have important controls on processes such as submarine groundwater discharge, sea water intrusion, and groundwater discharge to coastal springs and wetlands. We investigated seasonal variations in salinity in a groundwater‐fed coastal wetland (the RAMSAR listed Piccaninnie Ponds in South Australia) and found that salinity peaked during winter, coincident with seasonal sea level peaks. Closer examination of salinity variations revealed a relationship between changes in sea level and changes in salinity, indicating that sea level–driven movement of the fresh water‐sea water interface influences the salinity of discharging groundwater in the wetland. Moreover, the seasonal control of sea level on wetland salinity seems to override the influence of seasonal recharge. A two‐dimensional variable density model helped validate this conceptual model of coastal groundwater discharge by showing that fluctuations in groundwater salinity in a coastal aquifer can be driven by a seasonal coastal boundary condition in spite of seasonal recharge/discharge dynamics. Because seasonal variations in sea level and coastal wetlands are ubiquitous throughout the world, these findings have important implications for monitoring and management of coastal groundwater–dependent ecosystems.     

A Compatible Single-Phase/Two-Phase Numerical Model: 1. Modeling the Transient Salt-Water/Fresh-Water Interface Motion

Abstract A numerical model (NEWVAR) to simulate the transient movement of a discrete interface between salt water and fresh water has been developed. NEWVAR is designed to allow the analysis of a regional two-dimensional ground-water flow in coastal aquifers. The numerical solution permits the prediction of both regional fresh-water levels and two-dimensional fresh-water/salt-water interface by using nested square meshes.
The numerical solution is based on the finite-difference method; the Gauss-Jordan direct method is used for solving steady- and unsteady-state linear equations. Different procedures are used to avoid numerical difficulties in the transient position of the interface toe for two-dimensional areal flow.
The numerical solution was tested against the analytical ones for the cases of an advancing interface and of a floating fresh-water lens over sea water. These tests showed good agreement, thus verifying the finite-difference approximation. The results of an application of this model to a real aquifer are discussed in a companion paper entitled: "A Compatible Single-Phase/Two-Phase Numerical Model 2. Application to a Coastal Aquifer in Mexico."     

An improved pseudo-static method for seismic resistant design of underground structures

This paper describes a commonly used pseudo-static method in seismic resistant design of the cross section of underground structures. Based on dynamic theory and the vibration characteristics of underground structures, the sources of errors when using this method are analyzed. The traditional seismic motion loading approach is replaced by a method in which a one-dimensional soil layer response stress is differentiated and then converted into seismic live loads. To validate the improved method, a comparison of analytical results is conducted for internal forces under earthquake shaking of a typical shallow embedded box-shaped subway station structure using four methods： the response displacement method, finite element response acceleration method, the finite element dynamic analysis method and the improved pseudo-static calculation method. It is shown that the improved finite element pseudo-static method proposed in this paper provides an effective tool for the seismic design of underground structures. The evaluation yields results close to those obtained by the finite element dynamic analysis method, and shows that the improved finite element pseudo-static method provides a higher degree of precision.